Direct-product-closed subgroup property

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This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

Definition with symbols

A subgroup property p is said to be direct-product-closed if whenever H_1 \le G_1 satisfies p, and H_2 \le G_2 satisfies p, then H_1 \times H_2 satisfies p as a subgroup of G_1 \times G_2.

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties

Related metaproperties